Study On The Structure Characteristics Of G_λ Measure And The Application Of Fuzzyanalysis Method

The structure characteristics of Fuzzy measure and Fuzzy integral have beenhot topics until their definitions are proposed. In particular, many properties of gAmeasure have been obtained such as self-duality, convergence in measure,monotonicity，etc. However, to the best of author’s knowledge, there has not beenmuch work under taken on the convergence in gA measure. Therefore，it isnecessary to discuss the convergence in (pseudo-in) measure. Furthermore, theFuzzy analysis method has been widely applied to many fields recently. Theapplication has been received considerable attention in agricultural production, andmany classes evaluation systems have been established, and a large amount of therelated results on these topics have a guiding_λsignificance for the productionpractice.The problems are proposed as follows:Firstly，we aim to investigate a class of properties for gA measure. Theconcept of fundamental sequence in (pseudo-in) measure and the related propertiesof convergence in (pseudo-in) measure are given for gA measure. A larger numberof important results obtained. To mention a few, convergence almost (pseudo-almost)uniform is convergence in (pseudo-in) measure, convergence almost uniform mustbe convergence almost everywhere, convergence in measure then the subsequenceof the sequence of measurable functions must be convergence almost everywhere.Secondly, by applying_λthe Fuzzy analysis methods, the main representativereasons are presented for the impact on China’ grain production. Based on clusteirnganalysis approach，the practical measured data is obtained. Then，by using_λthemulti-factor comprehensive evaluation, the weight of each influence factors aregiven respectively and the relate factors which have an important influence to grainproduction are proposed. Finally, the results are given to provide a reliable theory basis of how to improve our country’s grain production.